Linganisha mbinu

	Modeli wa SARIMA Usiohusisha Mstari	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)	Mfumo wa SARIMA
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	1990–2000	1970	1970 (first edition); 1976 (revised)
Mwanzilishi	Tong (1990) for threshold nonlinear extensions; Franses & van Dijk (2000) for empirical finance applications	George Box and Gwilym Jenkins	Box, Jenkins, and Reinsel
Aina	Nonlinear time series model	Time series forecasting model	Seasonal time series model
Chanzo asilia	Tong, H. (1990). Non-linear Time Series: A Dynamical System Approach. Oxford University Press. ISBN: 978-0198523000	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0130607744
Majina mbadala	NL-SARIMA, nonlinear seasonal ARIMA, threshold SARIMA, smooth transition SARIMA	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component
Zinazohusiana	3	6	5
Muhtasari	The Nonlinear SARIMA model extends the classical Seasonal ARIMA framework by replacing the linear conditional mean function with a nonlinear specification — such as threshold switching or smooth transition — while retaining seasonal differencing and lag structure. It is used when seasonal time series exhibit regime-dependent dynamics, asymmetric adjustment, or other nonlinear patterns that a linear model cannot capture.	The ARIMA(p,d,q) model is the standard workhorse for univariate time series forecasting. It combines autoregressive terms (past values), differencing to induce stationarity, and moving average terms (past shocks) into a unified linear framework. Developed by Box and Jenkins (1970), it remains one of the most widely applied models in econometrics and applied statistics.	SARIMA extends ARIMA by adding seasonal autoregressive and moving-average operators to capture repeating patterns at fixed intervals — such as monthly, quarterly, or annual cycles. Denoted SARIMA(p,d,q)(P,D,Q)s, it is the standard workhorse for univariate seasonal time series forecasting in econometrics, economics, and official statistics.